Quasi-newton based preconditioning and damped quasi-newton schemes for nonlinear conjugate gradient methods

Mehiddin Al-Baali, Andrea Caliciotti, Giovanni Fasano*, Massimo Roma

*المؤلف المقابل لهذا العمل

نتاج البحث: Conference contribution

8 اقتباسات (Scopus)

ملخص

In this paper, we deal with matrix-free preconditioners for nonlinear conjugate gradient (NCG) methods. In particular, we review proposals based on quasi-Newton updates, and either satisfying the secant equation or a secant-like equation at some of the previous iterates. Conditions are given proving that, in some sense, the proposed preconditioners also approximate the inverse of the Hessian matrix. In particular, the structure of the preconditioners depends both on low-rank updates along with some specific parameters. The low-rank updates are obtained as by-product of NCG iterations. Moreover, we consider the possibility to embed damped techniques within a class of preconditioners based on quasi-Newton updates. Damped methods have proved to be effective to enhance the performance of quasi-Newton updates, in those cases where the Wolfe linesearch conditions are hardly fulfilled. The purpose is to extend the idea behind damped methods also to improve NCG schemes, following a novel line of research in the literature. The results, which summarize an extended numerical experience using large-scale CUTEst problems, is reported, showing that these approaches can considerably improve the performance of NCG methods.

اللغة الأصليةEnglish
عنوان منشور المضيفNumerical Analysis and Optimization - NAO-IV, 2017
المحررونLucio Grandinetti, Mehiddin Al-Baali, Anton Purnama
ناشرSpringer New York LLC
الصفحات1-21
عدد الصفحات21
رقم المعيار الدولي للكتب (المطبوع)9783319900254
المعرِّفات الرقمية للأشياء
حالة النشرPublished - 2018
الحدث4th International Conference on Numerical Analysis and Optimization, NAO-IV 2017 - Muscat, Oman
المدة: يناير ٢ ٢٠١٧يناير ٥ ٢٠١٧

سلسلة المنشورات

الاسمSpringer Proceedings in Mathematics and Statistics
مستوى الصوت235
رقم المعيار الدولي للدوريات (المطبوع)2194-1009
رقم المعيار الدولي للدوريات (الإلكتروني)2194-1017

Other

Other4th International Conference on Numerical Analysis and Optimization, NAO-IV 2017
الدولة/الإقليمOman
المدينةMuscat
المدة١/٢/١٧١/٥/١٧

ASJC Scopus subject areas

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